this just happened to me on my MacBook. It's been having issues when I run it off the battery; it will just turn off randomly. but it was plugged in when the Zs just appeared and the screen went black. I pushed escape and the screen returned.
there is a warning in system preferences, though, that says I need to service the battery. I guess it's my fault somehow

Sounds like the graphics processor is over-heating, which can cause artifacts (which you describe as Z's)
Switch to HTML5 player on YouTube instead of Flash if that is what is being used, Flash is terrible for overheating video cards.

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